A variety V (that is not necessarily a complete intersection) of codimension k is a component of a complete intersection of codimension k defined by k general linear combinations of any generating set of the defining ideal of V.
This function automates the above construction.
i1 : R = CC[x,y,z]; |
i2 : F = {x*y, x^2 - y, x*z}; |
i3 : L = generalEquations(2,F) 2 o3 = {(.291061 + .996464*ii)x + (.878627 + .868574*ii)x*y + (.049867 + ------------------------------------------------------------------------ 2 .662939*ii)x*z + (- .291061 - .996464*ii)y, (.593785 + .348517*ii)x + ------------------------------------------------------------------------ (.491959 + .393244*ii)x*y + (.867342 + .238291*ii)x*z + (- .593785 - ------------------------------------------------------------------------ .348517*ii)y} o3 : List |